How can game theory be used to interpret first-order logic?

In the philosophy of logic, game theory provides an alternative to traditional Tarski-type semantics through a framework known as game-theoretic semantics. Rather than relying on static definitions of truth, this approach interprets the truth of a first-order sentence as the existence of a winning strategy for a verifier in a rule-governed game.12

These games are played "outdoors" among the individuals within a specific universe of discourse. In this context, the verification of a sentence involves a series of moves where the truth of complex formulas is determined by the outcome of subgames. For example, when evaluating a conditional statement, the game is divided into subgames for the antecedent and the consequent; the verifier succeeds if they possess a strategy that ensures the consequent is verified given the truth of the antecedent.13

This dynamic model is particularly useful for representing how language connects to reality, as it accounts for the availability of information—such as the objects or functions identified during earlier stages of a game—which can then be utilized in subsequent stages, mirroring the behavior of anaphoric pronouns in natural language.23